I'm a fan, too. I think I first heard them on streaming radio 181.fm's Chillout channel back in 2009. Sweet Tides was the first track I heard.

Soma FM's Groove Salad is good sometimes, as is DI.FM/RadioTunes Chillout station. I used to use Pandora for similar, but it was becoming repetitive. I like Spotify's radio feature now.

Thievery Corporation - Sweet Tides

Somewhere along the way, I happened across this track from Groove Armada, Mary.
It was only available on a Japanese import disc, which I splurged for, but here on YouTube for your listening pleasure... Somewhere around the 2 minute mark, it's got this really sweet little melodic bit. Some of this music seems like it belongs on the Soundtrack of Life, playing over slow motion scenes of feelgoodery.

I really like Thievery Corporation and have seen them live a few times. I've been listening to them for a long time so it's nice to see them getting some love here!

I think their "Mirror Conspiracy" album is the quintessential "Thievery sound". I highly recommend this album as an introduction to the group. I like their other albums too, but Mirror Conspiracy just nails that unmistakable style of theirs.

I should get some more of their stuff on vinyl, I only have a well worn copy of this: